Two expressions are "equivalent" if they have the same result for any values of the variable or variables.
An equation if both expressions are equal
Yes. That is the definition of an algebraic expression.
choosing a variable to represent one of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.
Expressions never have equality signs
An expression with a variable.
These two are both similar because they are both expressions.
operational definition of a manipulated variable
483h4yg3h45
operational definition of a manipulated variable
an algebraic expression
No
The coefficients of polynomials are the numbers in front of the variable expressions. Ex: In the polynomial: 3x^5 + 12x^2 - 45x + 134 the numerical coefficients are: 3,12,& -45